21 Triangles - 22 circles - 23 trig Flashcards
confusing concept
for any triangle, the sum of any two sides must be
greater than the third
technique
the golden rule of geometry problem is
to draw a picture
key formula
Pythagorean theorem
a^2 + b^2 = c^2
key formula
common triples right triangles:
3-4-5
6-8-10
5-12-13
7-24-25
8-15-17
key formula
special right triangles
45-45-90
30-60-90
key formula
45-45-90
x^2 + x^2 = (x√2)^2
key formula
30-60-90
x^2 + (x√3)^2 = (2x)^2
confusing concept
when two triangles have the same angles measures
their sides are proportional
key formula
π radians =
180 degrees
key formula
area of a circle
πr^2
key formula
circumference of a circle
2πr
key formula
arc length
2 π r (θ/360°)
key formula
area of a sector
πr^2 (θ/360°)
confusing concept
central angles have the same measure as
the arcs that they “carve out”
confusing concept
inscribed angles are half the measure of
arcs that they “carve out”
key formula
angles inscribed in a semicircle are always
90 degrees
confusing concept
a radius drawn to a line tangent to the circle is
perpendicular to that line
key formula
general equation of a circle in the xy-plane
(x - h)^2 + (y - k)^2 = r^2,
where (h,k) is the center of the circle and r is the radius
key formula
sin x
opposite/hypotenuse
key formula
cos x
adjacent/hypotenuse
key formula
tan x
opposite/adjacent
confusing concept
trigonometric functions are
ratios
confusing concept
sin 30 is always equal to
1/2
because all right triangles with a 30 degree angle are similar
key formula
SOH-CAH-TOA
sin, cos, tan
key formula
sin x =
cos (90 - x) or (π/2 - x)
key formula
cos x in terms of sin equals
sin (90 - x) or (π/2 - x)
confusing concept
signs of trig functions in quadrant I
sine, cosine, tangent are all POSITIVE
confusing concept
signs of trig functions in quadrant II
ONLY sine is positive
confusing concept
signs of trig functions in quadrant II
ONLY tangent is positive
confusing concept
signs of trig functions in quadrant IV
ONLY cosine is positive
key formula
ASTC
trig functions on the quadrants
key formula
sin 0 =
0
key formula
cos 0 =
1
key formula
tan 0 =
0
key formula
sin 90 =
1
key formula
cos 90 =
0
key formula
tan 90 =
undefined
technique
to find the value of a trig function for an angle w/o a calculator
- determine what the sign of the results should be (positive/negative)
- find the reference angle
e.g. if angle is 225, the reference angle is 225 - 180 = 45 - use 45-45-90 or 30-60-90 special right triangles to get trig value for reference angle
